# Evaluate $\lim_{n\to\infty}n\sin(2\pi \mathrm en!)$ [duplicate]

Evaluate $$\lim_{n\to\infty}n\sin(2\pi \mathrm en!)$$

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## marked as duplicate by amWhy, Claude Leibovici, Michael Hoppe, Asaf Karagila, egregMar 22 '14 at 15:28

Sentences "evaluate $x$" won't help you receive advises from people. Especially if you use exclamation marks. What have you tried? –  Ilya Jan 18 '13 at 9:16
Hint: What is the closest integer to $en!$? –  user27126 Jan 18 '13 at 9:28
I can tell the answer to the question is $2\pi$. I dont know how to do it. Help! –  asimath Jan 18 '13 at 9:37
Hint: If you write $${\rm e}=\sum_{k=0}^\infty {1\over k!}$$then $${\rm e}n!=({\rm integer})+{1\over n+1}+({\rm small\ number})$$
I think if we solve using this result we will get answer $2\pi$. –  asimath Jan 18 '13 at 10:05